Bayesian restricted analysis is an important analytical tool for statistical investigation when some knowledge exist about the system under study. In typical analyses, such knowledge are usually used in the form of some restrictions which are assumed to be true definitively, i.e., with one hundred percent certainty. While this might be true in some applications, in others it might be too restrictive. It is often the case in biomedical and epidemiological studies that although the investigator might believe in the restrictions, he or she might have reservations on them. In other words, the restrictions might be believable but no to one hundred percent certainty.